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Cosh






Mathematica Notation

Traditional Notation









Elementary Functions > Cosh[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving trigonometric and exponential functions > Involving algebraic functions of cos and exp > Involving ep z(a+b cos(d z))beta cosh(c z)





http://functions.wolfram.com/01.20.21.1323.01









  


  










Input Form





Integrate[E^(p z) (a + b Cos[d z])^\[Beta] Cosh[c z], z] == ((a + ((1/2) b (1 + E^(2 I d z)))/E^(I d z))^\[Beta] (E^((c + p) z) (c - p + I d \[Beta]) AppellF1[-((I (c + p - I d \[Beta]))/d), -\[Beta], -\[Beta], -((I (c + I d + p - I d \[Beta]))/d), -((b E^(I d z))/(a + Sqrt[a^2 - b^2])), (b E^(I d z))/ (-a + Sqrt[a^2 - b^2])] - E^((-c + p) z) (c + p - I d \[Beta]) AppellF1[(I (c - p + I d \[Beta]))/d, -\[Beta], -\[Beta], -((I (-c + I d + p - I d \[Beta]))/d), -((b E^(I d z))/(a + Sqrt[a^2 - b^2])), (b E^(I d z))/ (-a + Sqrt[a^2 - b^2])]))/((1 + (b E^(I d z))/(a - Sqrt[a^2 - b^2]))^ \[Beta] (1 + (b E^(I d z))/(a + Sqrt[a^2 - b^2]))^\[Beta])/ (2 (c + p - I d \[Beta]) (c - p + I d \[Beta]))










Standard Form





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MathML Form







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</ci> </apply> <apply> <plus /> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <apply> <plus /> <ci> c </ci> <ci> p </ci> </apply> <ci> z </ci> </apply> </apply> <apply> <plus /> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> p </ci> </apply> <apply> <times /> <imaginaryi /> <ci> d </ci> <ci> &#946; </ci> </apply> </apply> <apply> <ci> AppellF1 </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <apply> <plus /> <ci> c </ci> <ci> p </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> d </ci> <ci> &#946; </ci> </apply> </apply> </apply> <apply> <power /> <ci> d </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#946; </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#946; </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <apply> <plus /> <ci> c </ci> <apply> <times /> <imaginaryi /> <ci> d </ci> </apply> <ci> p </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> d </ci> <ci> &#946; 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Rule Form





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Date Added to functions.wolfram.com (modification date)





2002-12-18